Inpatient and Outpatient services: Complements or Substitutes

Hans Martinez

March 7, 2024

Introduction

What’s the question? Are inpatient and outpatient medical services complements or substitutes?
Why does it matter? Policy implications. If substitutes, we would like to incentivize utilization of less expensive outpatient services. If complements, protect consumers and ensure better insurance pricing.
How will I answer it? New method, old question. Use recently developed methods allowing for complementarity/substitutability of goods (Gentzkow 2007; Ershov, Laliberté, and Orr 2018; Allen and Rehbeck 2019)

Lit Rev

A quick review of the literature shows only a handful of papers looking into complementarity/substitutability in the health demand of outpatient and inpatient services (Wang, Yang, and Avendano 2022; Kato and Goto 2017; Zhou et al. 2011)
Methodologically they are very simple
Recent developments have improved significantly how to empirically learn better about complementarity (Gentzkow 2007; Ershov, Laliberté, and Orr 2018; Allen and Rehbeck 2019)

Model

Discrete Choice Model allowing for unobservable heterogeneity over whether the goods are substitutes or complements \[ \begin{aligned} u_0 &= 0 \\ u_A &= \delta_A + \alpha p_A+\nu_A \\ u_B &= \delta_B + \alpha p_B +\nu_B\\ u_{AB}&= u_A+u_B+\Gamma \end{aligned} \]
Where \(u_j\) utility; \(p_j\) prices, \(\delta_j\) mean utilities, \(\nu_j\) unobservable variation in utility, and \(\Gamma\) captures whether goods A and B are complements or substitutes.

Empirical Approach

Data: RAND Health Insurance Experiment
Simulation techniques (MCMC; ELVIS)

References

Allen, Roy, and John Rehbeck. 2019. “Identification with Additively Separable Heterogeneity.” Econometrica 87: 1021–54. https://doi.org/10.3982/ecta15867.

Ershov, Daniel, Jean-William Laliberté, and Scott Orr. 2018. “Mergers in a Model with Complementarity.” https://ssrn.com/abstract=3295232.

Gentzkow, Matthew. 2007. “Valuing New Goods in a Model with Complementarity: Online Newspapers.” American Economic Review 97.

Kato, Hirotaka, and Rei Goto. 2017. “Effect of Reducing Cost Sharing for Outpatient Care on Children’s Inpatient Services in Japan.” Health Economics Review 7. https://doi.org/10.1186/s13561-017-0165-3.

Wang, Yixiao, Wei Yang, and Mauricio Avendano. 2022. “Does Informal Care Reduce Health Care Utilisation in Older Age? Evidence from China.” Social Science & Medicine 306: 115123. https://doi.org/10.1016/j.socscimed.2022.115123.

Zhou, Zhongliang, Yanfang Su, Jianmin Gao, Ling Xu, and Yaoguang Zhang. 2011. “New Estimates of Elasticity of Demand for Healthcare in Rural China.” Health Policy 103. https://doi.org/10.1016/j.healthpol.2011.09.005.